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Giải bài tập 4.13 trang 87 SGK Toán 9 tập 1 - Cùng khám phá

Cánh tay rô-bốt đặt trên mặt đất và có vị trí như Hình 4.28. Tính độ cao của điểm A trên đầu cánh tay rô-bốt so với mặt đất.

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Đề bài

Cánh tay rô-bốt đặt trên mặt đất và có vị trí như Hình 4.28. Tính độ c💮ao của điểm 🦂A trên đầu cánh tay rô-bốt so với mặt đất.

Phương pháp giải - Xem chi tiết

Vì BM//NC (cùng vuông góc với BN) nên \(\widehat {CBM} = \widehat {BCN} = {32^o}\) (hai góc so le trong). Ta có: \(\widehat {ABM} = \widehat {CBA} - \widehat {BCM}\). Tam giác NBC vuông tại N nên \(NB = BC.\sin NCB\). Tam giác ABM vuông tại M nên \(AM = AB.\sin ABM\). Vậy độ cao của điểm A trên đầu cánh tay rô- bốt so với mặt đất là: \(h = CP + BN + AM\).

Lời giải chi tiết

Vì BM//NC (cùng vuông góc với BN) nên \(\widehat {CBM} = \widehat {BCN} = {32^o}\) (hai góc so le trong). Ta có: \(\widehat {ABM} = \widehat {CBA} - \widehat {BCM} = {53^o} - {32^o} = {21^o}\). Tam giác NBC vuông tại N nên \(NB = BC.\sin NCB = 60.\sin {32^o} \approx 31,8\left( cm \right)\). Tam giác ABM vuông tại M nên \(AM = AB.\sin ABM = 60.\sin {21^o} \approx 21,5\left( cm \right)\). Vậy độ cao của điểm A trên đầu cánh tay rô-bốt so với mặt đất là: \(h = CP + BN + AM \approx 17 + 31,8 + 21,5 \approx 70,3\left( cm \right)\)

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